{"paper":{"title":"Liouville theorems for the fractional Navier-Stokes equations with arbitrary asymptotic state at infinity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Changzhi Liu, Wenke Tan","submitted_at":"2026-06-30T15:12:13Z","abstract_excerpt":"We mainly consider a Liouville-type problem for the three dimensional stationary fractional Navier-Stokes equations with arbitrary asymptotic state $u_\\infty$ at infinity. When $u_\\infty\\neq 0$ and $\\frac{1}{2}\\leq s<1$, we prove a complete Liouville theorem by establishing some refined $L^p$ estimates for the velocity without relying on perturbation arguments. These new estimates are stronger than the $L^3$ estimates obtained by the classical perturbation framework, we thus can take $u$ as a test function and give a direct and simple proof of Liouville theorem while avoiding some technical fr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.31794","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.31794/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}